Problem: Solve for $x$. Enter the solutions from least to greatest. $6x^2 - 12x - 210 = 0$ $\text{lesser }x = $
Explanation: $\begin{aligned} 6x^2 - 12x - 210 &= 0 \\\\ 6(x^2-2x-35)&=0 \end{aligned}$ Now let's factor the expression in the parentheses. $x^2-2x-35$ can be factored as $(x+5)(x-7)$. $\begin{aligned} 6(x+5)(x-7)&=0 \\\\ x+5=0&\text{ or }x-7=0 \\\\ x=-5&\text{ or }x=7 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -5 \\\\ \text{greater }x &= 7 \end{aligned}$